This would happen because our Start/Sit Assistant is based on the percentage of experts who prefer Player A over Player B, whereas the Matchup tab's Optimal Lineup is strictly based on our Expert Consensus Rankings (ECR).
Note that the rankings from both tools exclude experts who haven't created rankings for all positions (i.e. QB, RB, WR, TE, FLEX, K, and DST).
For example, say we have 20 experts who have created rankings for each position. While 12 of the 20 experts prefer Player A over Player B (which explains the Lineup Assistant's result), the 8 experts who prefer Player B ranked him so much higher than Player A that he ended up having the higher ECR (which would explain the Matchup tab's result).